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Properties

Label 1150.2.s
Level $1150$
Weight $2$
Character orbit 1150.s
Rep. character $\chi_{1150}(31,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $2400$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.s (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{55})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1150, [\chi])\).

Total New Old
Modular forms 7360 2400 4960
Cusp forms 7040 2400 4640
Eisenstein series 320 0 320

Trace form

\( 2400 q + 8 q^{3} + 60 q^{4} - 12 q^{5} + 8 q^{7} + 68 q^{9} + O(q^{10}) \) \( 2400 q + 8 q^{3} + 60 q^{4} - 12 q^{5} + 8 q^{7} + 68 q^{9} - 8 q^{11} - 12 q^{12} + 16 q^{13} + 8 q^{14} - 38 q^{15} + 60 q^{16} - 12 q^{17} - 72 q^{18} - 20 q^{19} - 14 q^{20} + 8 q^{21} - 24 q^{22} + 126 q^{23} - 104 q^{25} - 28 q^{27} - 36 q^{28} - 24 q^{29} - 68 q^{30} + 24 q^{31} - 60 q^{33} + 8 q^{34} + 4 q^{35} + 68 q^{36} - 48 q^{37} + 16 q^{38} - 24 q^{39} + 8 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} + 136 q^{47} - 12 q^{48} - 200 q^{49} + 20 q^{50} - 32 q^{51} + 16 q^{52} - 16 q^{53} - 8 q^{55} + 8 q^{56} - 56 q^{57} - 36 q^{59} - 18 q^{60} + 20 q^{61} - 28 q^{62} - 28 q^{63} + 60 q^{64} - 98 q^{65} + 16 q^{66} + 12 q^{67} + 8 q^{68} + 270 q^{69} - 116 q^{70} - 192 q^{71} + 16 q^{72} - 32 q^{73} - 80 q^{74} + 478 q^{75} - 8 q^{77} - 28 q^{78} - 32 q^{79} - 14 q^{80} + 204 q^{81} - 120 q^{82} - 40 q^{83} + 8 q^{84} - 70 q^{85} + 44 q^{86} - 4 q^{87} + 16 q^{88} + 64 q^{89} - 56 q^{90} - 120 q^{91} - 6 q^{92} + 48 q^{93} + 16 q^{94} + 154 q^{95} - 72 q^{97} - 24 q^{98} - 148 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)